A faster algorithm for minimum cost submodular flows

This paper presents a cycle canceling algorithm for the submodular flow problem. The algorithm uses an assignment problem whose optimal solution identifies most negative vertex-disjoint cycles in the auxiliary network. The cost scaling version of this algorithm runs in O(n4h 1ognC) time, where n is the number of vertices, h is the time for computing an exchange capacity, and C is the maximum absolute value of arc costs. This improves the best previously known weakly polynomial bound due to Cunningham and Frank.

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